This textbook provides an introduction to the mathematics of randomness, consisting of the two subfields of probability theory and statistics. The stochastic concepts, models, and methods are motivated by typical application examples and then systematically developed. The necessary measure-theoretical framework is provided at an elementary level right from the start. Numerous exercises, some with solution sketches, illustrate and complement the text. The target audience includes mathematics students from the third semester onward, as well as scientists and computer scientists interested in the mathematical foundations of stochastic processes. The 5th edition has been revised and moderately supplemented.